pyörähdysellipsoidina

Pyörähdysellipsoidi, in English a spheroid or ellipsoid of revolution, is a quadric surface generated by rotating an ellipse around one of its axes. If the ellipse is rotated around its major axis, the resulting spheroid is called a prolate spheroid. If it is rotated around its minor axis, the resulting spheroid is called an oblate spheroid. Spheres are a special case of spheroids where the semi-major and semi-minor axes are equal.

The equation of a spheroid centered at the origin can be expressed in Cartesian coordinates. For a prolate spheroid generated by rotating the ellipse x²/a² + y²/b² = 1 (with a > b) around the x-axis, the equation is x²/a² + y²/b² + z²/b² = 1. For an oblate spheroid generated by rotating the same ellipse around the y-axis, the equation is x²/a² + y²/a² + z²/b² = 1. In general, the equation is of the form (x²/a²) + (y²/b²) + (z²/c²) = 1, where two of the semi-axes (a, b, c) are equal.

Spheroids are common shapes in nature and science. Many celestial bodies, such as planets and stars, are approximately spheroidal due to their rotation. The Earth, for instance, is an oblate spheroid, slightly flattened at the poles and bulging at the equator. In mathematics and physics, spheroids are used in various calculations and models, particularly in fields dealing with gravitational fields or fluid dynamics. The study of spheroids also extends to their surface area and volume calculations, which depend on the lengths of the semi-major and semi-minor axes.